With the advent of ever more effective forms of noise reduction headsets to reduce the environmental noise sounds that reach the ears of its user, and possibly impede the user's ability to use one or more features of the headset (e.g., listening to music, engaging in two-way communications, etc.), a growing need has been identified to in some way allow speech sounds of another person in the vicinity of the user to still reach the ears of the user so as to allow the user to carry on a conversation with that other person without removing at least a portion of it from at least one of the user's ears. This has led to the introduction of a “talk-through” (TT) functionality being added to such a headset that employs one or more filtering techniques to separate speech sounds of such another person from other environmental sounds, and to pass those speech sounds through whatever passive noise reduction (PNR) or active noise reduction (ANR) functionality is provided by such a headset, and onward to an ear of its user. Unfortunately, difficulties persist in the provision of both ANR and TT functionality arising from false triggering of audio compressors arising from certain relatively loud environmental sounds having relatively fast onset times (e.g., gun-shot sounds, sounds of explosions, etc.), or electrical noise arising from such events as electrostatic discharges that create pulses that resemble such relatively loud environmental sounds by also having relatively fast onset times.